Re: What isn't a tautology?

erite423@xxxxxxxx wrote: 
Douglas Theobald wrote:

So I guess I'm the "pro-tautology" dude.

For clarity, here is my reasoning, summarized from a thread
elsewhere:

Surely a definition is just another type of statement, a
declarative sentence making an assertion. Isn't a definition a
proposition that can be used as a premise in an argument? A
definition is just a statement (like Fa or Gb), and so it should
have a truth value. And in the case of stipulative definitions
(the type of definition I am concerned with), the truth value is
always T, by definition.


A definition is not a tautology and does not behave as a tautology.
Suppose you have a set of consistent premises, which contain no mention
of skirnobs. The following are two possible stipulative definitions of
"skirnob":

Definition 1: For all x, x is a skirnob if and only if x is shiny.
Definition 2: For all x, x is a skirnob if and only if x is not shiny.

The statements in definition 1 and 2 are mutually contradictory.
Nevertheless, you can add _either_ definition 1 _or_ definition 2 to
your premises without introducing any contradiction. Had, say,
definition 1 been a tautology, then definition 2 would have been a
logical contradiction and you couldn't add definition 2 to your
premises without making them inconsistent.


How, then, do you reconcile your argument with mine?

P1. A tautology is a statement whose column in a truth-table contains nothing but Ts.
P2. Stipulative definitions are true by definition.
C. A stipulative definition is a tautology.

I would say that your D1 and D2 are actually not mutually contradictory, because, after all, they are two different stipulative definitions. They must both be true, as D1 and as D2 -- skirnob (D1) is a different critter from skirnob (D2).


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Relevant Pages

  • Re: What isnt a tautology?
    ... And in the case of stipulative definitions ... A definition is not a tautology and does not behave as a tautology. ... Suppose you have a set of consistent premises, ... x is a skirnob if and only if x is shiny. ...
    (sci.logic)
  • Re: What isnt a tautology?
    ... And in the case of stipulative definitions ... >> A definition is not a tautology and does not behave as a tautology. ... For all x, x is a skirnob if and only if x is not shiny. ... So, if a formula in predicate logic is a tautology, then it is true ...
    (sci.logic)
  • Re: What isnt a tautology?
    ... A tautology is a statement whose column in a truth-table contains ... Stipulative definitions are true by definition. ... But not in virtue of their propositional logical form, ... tested in a truth table. ...
    (sci.logic)
  • Re: What isnt a tautology?
    ... declarative sentence making an assertion. ... have a truth value. ... And in the case of stipulative definitions ...
    (sci.logic)
  • Re: What isnt a tautology?
    ... A tautology is a statement whose column in a truth-table contains ... Stipulative definitions are true by definition. ... > But not in virtue of their propositional logical form, ... A* is a Herbrand disjunction or of the ...
    (sci.logic)